L Verdickt

SENSITIVITY ANALYSIS OF A ONE-DIMENSIONAL CONVECTION-DIFFUSION MODEL FOR SECONDARY SETTLING TANKS

ABSTRACT One-dimensional models describing the flow and settling process in secondary settling tanks have great potential with respect to process control. Most of these models are based on a conservation equation that is discretized by dividing the settler into a fixed number of horizontal layers. In this article, the focus is on convection-diffusion models, which—in contrast to other one-dimensional models—ensure mesh-independent concentration profiles. The sensitivity of a prototype convection-diffusion model with respect to its parameters and the loading and operational conditions is studied by means of steady-state simulations. Based on the results, the importance of each of the model parameters is assessed. For each combination of parameter values, loading conditions, and operational variables considered in the study, the minimum number of layers required to obtain a practically mesh-independent concentration profile is determined on the basis of a newly developed objective criterion. This analysis leads to the identification of those factors having a large influence on the numerical behavior of the model.

A linear ASM1 based multi-model for activated sludge systems

In the search for a reliable but simple model for the biodegradation processes of an activated sludge wastewater treatment plant, this paper presents a multi-model which is valid for the global operating region of a standard carbon and nitrogen removing facility. In a first step, locally valid linear models are derived. Two linearization procedures are compared. The first procedure is the classical Taylor series expansion, while the second is a newly developed linearization procedure based on weighted linear combinations. In a second step, the locally valid models are combined to obtain one globally valid multi-model. Previous work has focused on the most basic configuration of one anoxic and one aerated tank followed by a point settler [Smets, I.Y., Haegebaert, J.V. and Carrette, R. and Van Impe, J.F., 2003, Water Research, 37, 1831 – 1851]. Refinements to the methodology are however needed (and presented here) once the influent flow rate range is increased and the benchmark configuration, proposed by the COST 682 working group no. 2, is taken as the simulation protocol. The main advantage of the obtained linear model (structure) remains the alliance of high predictive power with low complexity, rendering the multi-model fit for on-line optimization and control schemes.

SIMULATION ANALYSIS OF A ONE-DIMENSIONAL SEDIMENTATION MODEL

Abstract One-dimensional models for describing the secondary settler in activated sludge wastewater treatment are important with respect to process control and optimization. The most widely used one-dimensional model nowadays is the model presented by Takacs et al. (1991). In this paper, the model of Takacs et al. is thoroughly studied at the simulation level. Simulations have been performed to analyze the dynamic behaviour of the concentration profile and to examine the influence on the steady state concentration profile of ( i ) the loading characteristics (influent concentration and flow rate), and ( ii ) the number of layers considered in the settler. The simulations reveal a major shortcoming of the Takacs model, namely, its inconsistency with respect to the number of layers considered in the discretized equations. The identification problem resulting from this inconsistency is clearly illustrated. As an alternative, the (consistent) model of Hamilton et al. (1992) is proposed.

Role of the diffusion coefficient in one-dimensional convection – diffusion models for sedimentation/thickening in secondary settling tanks

In this paper, the role of the diffusion coefficient in one-dimensional convection – diffusion models for secondary settling tanks is addressed. A simulation analysis is performed using a representative convection – diffusion model to demonstrate the large sensitivity of the model solutions with respect to the value of the diffusion coefficient. In addition, it is illustrated that the numerical behaviour of the model is strongly influenced by the value of the diffusion coefficient. As the results of the simulation study clearly demonstrate the crucial role of the diffusion coefficient in convection – diffusion models, accurate calibration of the diffusion coefficient is of utmost importance when using such models. Therefore, a new closure for the evaluation of a spatially dependent diffusion coefficient is introduced and analysed.

On the Number of Grid Layers Required for Accurate Simulation of a Convection-Diffusion Model for Secondary Settling Tanks

Abstract One-dimensional models that can adequately describe the flow and settling process in secondary settling tanks (SSTs) are an important tool with respect to control and optimisation of activated sludge wastewater treatment systems. In this study, the focus is on the one-dimensional convection-diffusion model proposed by Hamilton et al. (1992). Like most one-dimensional sedimentation models, it is based on a mass balance equation, which is discretized by dividing the settler into a number of horizontal layers with equal height. The advantage that convection-diffusion models have over most other one-dimensional models is that they generate mesh independent concentration profiles. Nevertheless, a minimal number of layers nmin is required to ensure convergence of the concentration profiles with respect to the number of layers. In this paper, the required number of layers is determined for a wide range of loading and operational conditions, and the sensitivity of n min with respect to the model parameters is assessed. The required number of layers is shown to depend strongly on the operational status of the settling tank and on the value of the diffusion coefficient

Towards a Linear ASM1 Based Multi-Model for the Activated Sludge Process: Validation with Benchmark Simulations

Abstract In the search for a reliable but simple model for the biodegradation processes of an activated sludge wastewater treatment plant, this paper presents a linear multi-model which is valid for the global operating region of a standard carbon and nitrogen removing facility. The overall procedure, consisting of three steps (i.e., data generation, local model linearization and model interpolation) has been introduced in previous work (see, e.g.,(Smets et al., 2003b)) for the most basic configuration of one anoxic and one aerated tank followed by a point settler. Refinements to the methodology are however needed (and presented here) once the influent flow rate range is increased and the benchmark configuration, proposed by the COST 682 working group no. 2, is taken as the simulation protocol. The main advantage of the obtained linear model (structure) remains the alliance of high predictive power with low complexity, rendering the model fit for on-line optimization and control schemes.